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From: Jeremy Bruestle (jeremy.bruestle_at_[hidden])
Date: 2007-06-29 16:09:52


I have developed a C++ tensor library using template expressions which
allows Einstein summation convention to be used to describe
mathematical operations on tensors in C++. This allows a great
simplification in syntax, while retaining execution speeds identical
to hand optimized C code in most cases. An example of the syntax is:

// Declare three rank 2 tensors (rank = # of dimensions) of doubles
with sizes of
// 6 x 5, 6 x 10, and 10 x 5 respectively

tensor<double, 2> A(6, 5);
tensor<double, 2> B(6, 10);
tensor<double, 2> C(10, 5);

// Name three index variable to be used in what follows
index_variable<0> i;
index_variable<1> j;
index_variable<2> k;

A[i][j] = 1.0; // Initialize A to all 1's
B[i][j] = 4.5; // Initalize B to all 4.5

boost::mt19937 rng;
C[i][j] = trand(rng); // Initalize C to uniform random numbers 0-1
C[i][2] = 2.1; // Set row 2 to 2.1
C[2][i] = 5.5; // Set col 2 to 5.5
C[2][2] = 0.0; // Zero out 2,2

A[i][j] = B[i][k] * C[k][j]; // Perform a matrix multiply

/* The above line translates roughly as:
for(size_t i = 0; i < A.size<0>(); i++)
  for(size_t j = 0; j < A.size<1>(); j++)
    double total = 0.0;
    for(size_t k = 0; k < B.size<1>(); k++)
      total += B[i][k] * C[k][j];
    A[i][j] = total;
An unlimited number of dimensions are supported, arbitrary operations
are allowed, and for cases where you wish to perform other types of
cumulative functions, such as finding the maximum element, a syntax
such as: A[i] = max(j, B[i][j]); is allowed. There are lots of other
interesting features but I don't wish to make this email too long.

As far as efficency, Intel's compiler builds every example I've tried
so far into code as good as doing the work by hand. GCC does so for
expressions of reasonably complexity, and MSVC's optimizer does
alright, but not nearly as well as the others.

I was interested in knowing what the interest level of providing such
a library as part of boost would be. I've tried to adhere to the
boost coding guidelines during the construction. I've been using this
library for over 6 months myself for scientific computing. However,
I've so far avoiding sending a query to the boost mailing lists as the
procedures for submission and review seem quite daunting. I'm usually
crushingly busy, and I'm also especially bad at documentation. Still,
I thought I would float the idea to guage interest, and also ask if
anyone would be interested in helping me through the process somewhat.

Thank you for you time.

-Jeremy Bruestle

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